Charles Darwin once said that he didn't understand science until he studied geology. How was Lyell’s way of thinking about slow---->?

Charles Lyell and Charles Darwin were actually close friends. Lyell introduced the theory of uniformitarianism to Darwin, the suggestion that what we see happening today is what happened in the past. The geology motto goes, "The present is the key to the past." Which is to say that if we see, say, a waterfall eroding back up stream today, then that's exactly how waterfalls eroded a million years ago. Darwin took this one step farther and introduced it to biology/botany and geology hand in hand. And it's true, life develops slowly, with catastrophic events punctuating it -- catastrophic geologic events. This is called punctuated equilibrium, and rides on top of Lyell's uniformitarianism.

When environments change slowly they give the organisms that inhabit them the time necessary to adapt to their change. For example, a volcano erupts on an island and its ash cloud blocks out the sun. The island will inevitably get colder, and many of the plants and cold-blooded animals living there will die. In contrast, an island is gradually pushed away from the equator due to shifting in tectonic plates, a process that takes millions of years. This would give species on the island plenty of time to adapt to the incrementally dropping temperatures (perhaps the plants would grow thicker bark, develop smaller cold-hardier leaves, and the lizards would become warm-blooded or learn to live deep underground) and survive.